

A211561


T(n,k) = number of nonnegative integer arrays of length n+k1 with new values 0 upwards introduced in order, and containing the value k1.


12



1, 1, 2, 1, 4, 5, 1, 7, 14, 15, 1, 11, 36, 51, 52, 1, 16, 81, 171, 202, 203, 1, 22, 162, 512, 813, 876, 877, 1, 29, 295, 1345, 3046, 4012, 4139, 4140, 1, 37, 499, 3145, 10096, 17866, 20891, 21146, 21147, 1, 46, 796, 6676, 29503, 72028, 106133, 115463, 115974, 115975
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OFFSET

1,3


COMMENTS

Table starts
....1.....1......1......1.......1........1........1.........1..........1
....2.....4......7.....11......16.......22.......29........37.........46
....5....14.....36.....81.....162......295......499.......796.......1211
...15....51....171....512....1345.....3145.....6676.....13091......24047
...52...202....813...3046...10096....29503....77078....183074.....401337
..203...876...4012..17866...72028...256565...810470...2300949....5957407
..877..4139..20891.106133..503295..2134122..8016373..26869727...81381744
.4140.21146.115463.649045.3513522.17337685.76199007.298009584.1046405027


LINKS



FORMULA

Empirical: T(n,k) = Sum_{j=k..n+k1} stirling2(n+k1,j)


EXAMPLE

Some solutions for n=5, k=4:
..0....0....0....0....0....0....0....0....0....0....0....0....0....0....0....0
..1....1....1....0....1....1....1....1....0....1....1....1....1....1....1....0
..1....2....2....0....0....2....2....0....1....2....2....2....2....0....2....1
..2....0....2....0....2....0....3....2....2....2....3....3....2....2....0....2
..3....1....3....1....3....2....1....3....3....2....1....3....3....2....1....2
..4....0....3....0....3....3....4....1....3....3....0....2....4....3....2....2
..5....3....3....2....4....4....2....1....2....2....1....0....4....3....3....2
..2....0....1....3....5....4....4....4....4....2....0....4....3....1....2....3


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STATUS

approved



